ThmDex – An index of mathematical definitions, results, and conjectures.
F10518
Formulation 0
Let $X \in \mathsf{Random}(\to [-\infty, \infty])$ be a D4381: Random basic number.
Then $|X| \overset{a.s.}{<} \infty$ if and only if
(1) \begin{equation} X^+ \overset{a.s.}{<} \infty \end{equation}
(2) \begin{equation} X^- \overset{a.s.}{<} \infty \end{equation}